prove lebhintz theorem
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The other leibnitz theorem is computing nth derivative of product of two functions.I am attaching an example as well for better understanding.
Leibnitz’s Theorem :
It provides a useful formula for computing the nth derivative of a product of two functions.
Statement : If u and v are any two functions of x with un and vn as their nth derivative. Then the nth derivative of uv is
(uv)n = u0vn + nC1 u1vn-1 + nC2u2vn-2 + …+nCn-1un-1v1+unv0
Note : We can interchange u & v (uv)n = (vu)n,
nC1 = n , nC2 = n(n-1) /2! , nC3= n(n-1)(n-2) /3!
Leibnitz’s Theorem :
It provides a useful formula for computing the nth derivative of a product of two functions.
Statement : If u and v are any two functions of x with un and vn as their nth derivative. Then the nth derivative of uv is
(uv)n = u0vn + nC1 u1vn-1 + nC2u2vn-2 + …+nCn-1un-1v1+unv0
Note : We can interchange u & v (uv)n = (vu)n,
nC1 = n , nC2 = n(n-1) /2! , nC3= n(n-1)(n-2) /3!
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